Scatterplots with Penguins

The graphs below don’t have proper titles, axis labels, legends, etc. Please take care to do this on your own graphs. Throughout this demo we will use the palmerpenguins dataset. To access the data, you will need to install the palmerpenguins package:

install.packages("palmerpenguins")

Geometric layer

We use geom_point() to generate scatterplots (requires x and y aes)

library(tidyverse)
library(palmerpenguins)
data(penguins)

penguins %>%
  ggplot(aes(x = bill_depth_mm, y = bill_length_mm)) +
  geom_point()

Always adjust transparency!

Scatterplots display the joint distribution of the variables along the x and y axes. You should always adjust the transparency of points via alpha to visualize overlap - providing a better understanding of joint frequency. This is especially important with larger datasets.

penguins %>%
  ggplot(aes(x = bill_depth_mm, y = bill_length_mm)) +
  geom_point(alpha = 0.5)

Mapping Aesthetics

Colors

We can color by a third variable (e.g., different color for each category).

Note that, just like the x and y aesthetics, you can put color = inside ggplot or geom_point - both display the same visualization:

penguins %>%
  ggplot(aes(x = bill_depth_mm, y = bill_length_mm, color = species)) +
  geom_point(alpha = 0.5)

penguins %>%
  ggplot(aes(x = bill_depth_mm, y = bill_length_mm)) +
  geom_point(alpha = 0.5, aes(color = species))

You can also color by a quantitative variable using a color scale/gradient:

penguins %>%
  ggplot(aes(x = bill_depth_mm, y = bill_length_mm)) +
  geom_point(alpha = 0.5, aes(color = body_mass_g))

The default color gradient is not the most appealing, while there are a number of possibilities - blue to orange is a good choice since these colors are opposites on the color spectrum:

penguins %>%
  ggplot(aes(x = bill_depth_mm, y = bill_length_mm)) +
  geom_point(alpha = 0.5, aes(color = body_mass_g)) +
  scale_color_gradient(low = "darkblue", high = "darkorange")

Point size (size)

We can also map variables to other aesthetics, e.g. size:

penguins %>%
  ggplot(aes(x = bill_depth_mm, y = bill_length_mm)) +
  geom_point(alpha = 0.5, aes(size = body_mass_g))

Point type (shape)

… or the type (shape) of points:

penguins %>%
  ggplot(aes(x = bill_depth_mm, y = bill_length_mm)) +
  geom_point(alpha = 0.5, aes(shape = species))

Combining aesthetics

We can even do several of these at once:

penguins %>%
  ggplot(aes(x = bill_depth_mm, y = bill_length_mm,
             color = species, shape = island,
             size = body_mass_g)) +
  geom_point(alpha = 0.5)

The above graph may be a bit difficult to read, but it contains a lot of information in the sense that it is a 5-dimensional graphic:

  • x = bill depth (mm)
  • y = bill length (mm)
  • color = species
  • size = body mass (g)
  • shape = island

But be careful!

The more complications you add, the more difficult your graph is to explain.

Trend Lines

We can do different forms of statistical modeling within our plots (e.g., with geom_smooth()).

For example, we can add a linear regression line to our plot very easily. For this example, we’ll switch to looking at body_mass_g against flipper_length_mm.

Linear regression

To do this, we can use + geom_smooth(method = lm):

penguins %>%
  ggplot(aes(x = flipper_length_mm, y = body_mass_g)) +
  geom_point(alpha = 0.5) + 
  geom_smooth(method = "lm", se = FALSE)

Linear regression (with error bars)

Above, I added se = FALSE so that the standard error bars do not show up in the graph. Setting this parameter to TRUE produces (by default) 95% confidence intervals.

penguins %>%
  ggplot(aes(x = flipper_length_mm, y = body_mass_g)) +
  geom_point(alpha = 0.5) + 
  geom_smooth(method = "lm", se = TRUE)

You can change the level of the confidence intervals using the level argument:

penguins %>%
  ggplot(aes(x = flipper_length_mm, y = body_mass_g)) +
  geom_point(alpha = 0.5) + 
  geom_smooth(method = "lm", se = TRUE, level = 0.99)

However, from these graphs, it’s not clear if the linear regression is a good fit. We can “eyeball” this by looking at the fitted versus residuals, or we can make a residual-versus-fit plot.

What’s a residual-versus-fit plot? In short, the “fits” are the estimated y-values from the linear regression (i.e., the y-values along the linear regression line). Meanwhile, the “residuals” are the distance between the actual y-values and the fits. A residual-versus-fit plot is itself a scatterplot, with fits on the x-axis and residuals on the y-axis.

lin_reg <- lm(body_mass_g ~ flipper_length_mm, data = penguins)
fitted_vals <- fitted(lin_reg)
res_vals <- residuals(lin_reg)
tibble(fits = fitted_vals, 
       residuals = res_vals) %>%
  ggplot(aes(x = fits, y = residuals)) +
  geom_point() +
  geom_hline(yintercept = 0, linetype = "dashed", color = "red")

We look for two things when looking at residual-versus-fit plots:

  • Is there any trend around the 0 horizontal line? If so, that might be a violation of the linearity assumption (more on this next class).
  • Do the points have equal vertical spread from left to right? If not, that might be a violation of the equal variance assumption.

We’ll talk about these assumptions more next class.

Variable Transformations

Transformations of the Outcome

We can transform variables as well – again, within the plot. First, we will focus on the outcome y; in particular, we will focus on log transformations. This can be done through the y argument…

penguins %>%
  ggplot(aes(x = flipper_length_mm, y = log(body_mass_g))) +
  geom_point(alpha = 0.5) + 
  geom_smooth(method = "lm", se = TRUE)

Transformations of Covariates

It’s also possible to include transformations of the covariates instead of (or in addition to) transformations of the outcome. For example, the following plots a quadratic regression model (i.e., plots y ~ x + x^2).

Note that the formula argument in geom_smooth requires you to write in terms of y and x, NOT the variable names!

penguins %>%
  ggplot(aes(x = flipper_length_mm, y = body_mass_g)) +
  geom_point(alpha = 0.5) + 
  geom_smooth(method = "lm", 
              formula = y ~ x + I(x^2))

To assess if this is a better fit, we can again make a fitted-versus-residual plot (this looks better!):

quad_lin_reg <- lm(body_mass_g ~ flipper_length_mm + I(flipper_length_mm^2), 
                   data = penguins)
quad_fitted_vals <- fitted(quad_lin_reg)
quad_res_vals <- residuals(quad_lin_reg)
tibble(fits = quad_fitted_vals, 
       residuals = quad_res_vals) %>%
  ggplot(aes(x = fits, y = residuals)) +
  geom_point() +
  geom_hline(yintercept = 0, linetype = "dashed", color = "red")

Leave The Points. Take The Regression Model. (But generally this is a bad idea…)

We don’t even need to plot the points to do this – you can plot the regression model by itself by simply omitting geom_point():

penguins %>%
  ggplot(aes(x = flipper_length_mm, y = body_mass_g)) +
  geom_smooth(method = "loess")

As always, you can adjust some parameters (like color, alpha, etc.):

penguins %>%
  ggplot(aes(x = flipper_length_mm, y = body_mass_g)) +
  geom_smooth(method = "loess", se = TRUE, fill = "darkorange", 
              color = "darkblue", size = 2, alpha = 0.2) +
  theme_bw()

However, in general I don’t recommend doing this, because it hides the data entirely, making it unclear which data points are influencing the regression line.